''The crest has passed,'' says David Devlin, an economist with the Institute for International Finance, a body set up by international banks to research the crisis. ''But you still have some 'wavelets,' like Argentina.'' (Argentina has not yet completed negotiations with the International Monetary Fund on a domestic austerity program necessary to obtain needed new loans.)

William R. Cline, a senior fellow at the Institute for International Economics in Washington, says that in purely economic terms, ''fundamental debt recovery is proceeding well.''

''But,'' he adds, ''political perceptions in debtor countries nonetheless remain relatively negative, and the debtor problem is by no means resolved.''

So he sees a paradox between favorable economic trends and escalation of political pressure for some form of debt relief.

Mr. Brautigam bases his increased optimism partly on the fact that commercial banks and governments are recognizing that they must to some degree share the burdens of economic adjustment with the debtor nations.

He notes that the banks, currently negotiating with Mexico, expect to reschedule several years of debt payments rather than only one year. They also will offer a concession in the way of a narrower spread between what their money costs them in terms of interest, and the interest rate they charge Mexico. He also hopes that governments will not step up protectionist measures against imports from the debtor nations.

Evidence of a better economic scene for the debtor nations includes the following:

* The global recession, which precipitated the crisis, has been replaced by a sustained international recovery. Growth this year in the industrialized countries should reach about 4 percent. For the whole world, growth in output should run 2.5 to 3 percent. This, says economist Cline, ''is the central ingredient in the recipe for resolving the debt problem.'' Industrial countries import more when their economies are thriving.

* The 19 largest debtors cut their external deficits (on what is called the current account) from $56 billion in 1982 to $23 billion in 1983. Much of this was achieved by trimming imports. Now exports are growing rapidly.

In the first four months of 1984, Mexico's non-oil exports were up by 56 percent from the same period in 1983. Brazil's exports of manufactured goods were up 68 percent in the same four months. Mr. Cline says Mexico's trade surplus has been running at a rate of $15 billion yearly, and Brazil's at $12 billion. Brautigam estimates Argentina's trade surplus this year to be about $3. 8 billion, but that nation needs some $5.9 billion to pay interest on its debts.

* There are signs of economic recovery in Latin America. The region's output fell by 3.3 percent in 1983, leaving per capita income some 9 percent below its 1980 level. This year, however, industrial production has been rising by some 3. 8 percent in Mexico and 2.2 percent in Brazil.

Cline says growth rates should return to 4 to 6 percent in the area in 1985 and beyond.

One negative factor in the debt crisis was the rise in interest rates this spring, when the prime rate of commercial banks (the basic interest rate charged business customers) in the United States went up to 13 percent. About $380 billion of the debt of non-OPEC developing countries is interest-sensitive; that is, as rates go up in New York or London, the interest on such loans automatically rises.

Thus, a 1 percent rise in lending nations' interest rates costs debtor nations $3.8 billion yearly. But Cline calculates ''conservatively'' that an extra 1 percent growth in the industrial countries boosts the exports of the non-oil exporting, developing countries by about $12 billion. That's three times the impact of a 1 percent interest rate hike.

Since growth of the industrial countries will have risen about 1.7 percent this year above the growth rate of 1983, export earnings will more than make up for about a 2 percent rise in interest charges this year, Cline reckons.

''The political impact of the highly visible interest-rate increase is understandable,'' he said. ''But it overstates the real economic damage of higher interest rates by failing to take into account the broader international economic environment.''

Messrs. Devlin and Brautigam hope that Mexico will be in good enough financial shape next year that commercial banks will once more voluntarily lend to it, rather than having to lend to it as part of a negotiated debt rescheduling operation. Brazil, they figure, would be next to return to ''normal'' among the major debtors. Argentina could take longer.

Stocks of the major American banks holding the bulk of the loans to the largest Latin American debtors are still at extremely low levels. ''Markets are both manic-depressive and lagging,'' said Mr. Devlin, who was secunded from Citibank, one of the largest lenders to developing nations.

Investors may still be fearful of political unrest in the debtor nations - unrest that may prompt a moratorium or default on interest repayments. ''Political frustration is currently a greater risk than economic setbacks,'' said Cline. But that risk is hard to measure.